Hi guys I can't do the last part of this question so thanks if anybody could help!

Find the first four terms, in ascending order, in the expansion of (1-2x)^-2. State the values of x for which this expansion is valid.

Hence,

(i) by choosing a suitable value of x, find sum to infinity (starting value r=1) of r/2^(r-1),

(i) show that [sq root 2 cos (2x+(pi/4))] / (1-2tanx)^2 is estimated to be 1+2x+2x^2, given that x is small enough for its third and higher powers to be ignored.

Many apologies for the 'messiness'!